sensors Article
A Simulation Study of a Radiofrequency Localization System for Tracking Patient Motion in Radiotherapy Mark Ostyn 1,2 , Siyong Kim 1 and Woon-Hong Yeo 2,3, * 1
2 3
*
Radiation Oncology, Medical Physics Graduate Program, School of Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA;
[email protected] (M.O.);
[email protected] (S.K.) Department of Mechanical and Nuclear Engineering, School of Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA Center for Rehabilitation Science and Engineering, School of Medicine, Virginia Commonwealth University, Richmond, VA 23298, USA Correspondence:
[email protected]; Tel.: +1-804-827-3517; Fax: +1-804-827-7030
Academic Editors: Changzhi Li, Roberto Gómez-García and José-María Muñoz-Ferreras Received: 10 February 2016; Accepted: 11 April 2016; Published: 13 April 2016
Abstract: One of the most widely used tools in cancer treatment is external beam radiotherapy. However, the major risk involved in radiotherapy is excess radiation dose to healthy tissue, exacerbated by patient motion. Here, we present a simulation study of a potential radiofrequency (RF) localization system designed to track intrafraction motion (target motion during the radiation treatment). This system includes skin-wearable RF beacons and an external tracking system. We develop an analytical model for direction of arrival measurement with radio frequencies (GHz range) for use in a localization estimate. We use a Monte Carlo simulation to investigate the relationship between a localization estimate and angular resolution of sensors (signal receivers) in a simulated room. The results indicate that the external sensor needs an angular resolution of about 0.03 degrees to achieve millimeter-level localization accuracy in a treatment room. This fundamental study of a novel RF localization system offers the groundwork to design a radiotherapy-compatible patient positioning system for active motion compensation. Keywords: radiotherapy; localization; direction of arrival; angulation; Monte Carlo simulation; intrafraction motion
1. Introduction External beam radiation therapy is one of the most significant tools available in modern cancer treatment. Linear accelerators generate high-energy photons and careful planning directs the output into patient tumors. These X-rays introduce an ionizing dose of radiation into matter along the path of the beam. The received dose damages DNA at the molecular level, which increases the likelihood of cell death. Healthy tissue along the beam path is spared from receiving excessive dose by spreading dose delivery over several beam angles (Figure 1a). Most treatments deliver the cumulative dose in a series of 15–30 min fractions over the course of 2–8 weeks, which grants healthy tissue sufficient time for DNA repair. New delivery techniques, such as intensity-modulated radiation therapy or volume-modulated arc therapy, allow precise delivery of the dose to a set volume in space, conforming to the shape of the tumor and sparing healthy tissue. These types of treatments are often characterized by steep dose gradients between the target region and normal tissue, which necessitates accurate positioning during treatment. Precise information about the position, orientation, and motion of the tumor is often unknown during dose delivery. Thus, oncologists prescribe a volumetric margin of necessary size
Sensors 2016, 16, 534; doi:10.3390/s16040534
www.mdpi.com/journal/sensors
Sensors 2016, 16, 534
2 of 11
to deliver the prescribed dose to the disease site volume, for a given level of spatial uncertainty [1]. Sensors 2016, 16, 534 2 of 11 with Larger margins increase the amount of healthy tissue receiving cell-lethal dose and may overlap critical organs such as the brain, lungs, heart, or bowels. Thus, modern treatment planning requires critical organs such as the brain, lungs, heart, or bowels. Thus, modern treatment planning requires sufficiently large margins to ensure tumor coverage as well as necessarily small margins to avoid sufficiently large margins to ensure tumor coverage as well as necessarily small margins to avoid delivering excess dose to to healthy thespatial spatial uncertainties be well delivering excess dose healthytissue. tissue. The The magnitude magnitude ofofthe uncertainties mustmust be well known and and minimized. known minimized.
Figure 1. (a) Example of conformal radiotherapy for targeting a brain tumor; (b,c) Schematic
Figure 1. (a) Example of conformal radiotherapy for targeting (b,c) Schematic illustrations for a patient receiving external beam radiation therapy aforbrain brain tumor; cancer. Initially, the illustrations for a patient receiving external beam radiation therapy for brain cancer. Initially, beam is delivered to the right target with a good alignment (b), but the motion causes the head the beammisalignment is delivered(c), towhich the right target with a good alignment (b), but the motion causes the head makes an error relative to the planned delivery. misalignment (c), which makes an error relative to the planned delivery. The most notable sources of uncertainty are improper alignment of a patient with the prescribed field. An example in Figure 1b,c shows intrafraction motion, caused by patient movement during The most notable sources of uncertainty are improper alignment of a patient with the prescribed the treatment. Setup errors have been minimized by employment of immobilization equipment and field. An example in Figure 1b,c shows intrafraction motion, caused by patient movement during alignment of fiducial markers with static laser grids, but intrafraction motion has only recently been the treatment. Setupsystems, errors such haveasbeen minimized employment of immobilization studied. Optical surface tracking by [2–6] or marker tracking [7], have beenequipment used and alignment of fiducial markers with static laser grids, but intrafraction motion has only successfully to monitor intrafraction motion in several disease sites. However, these systems are recently not been robust studied. Optical systems, such as tracking [2–6] orline-of-sight marker tracking [7], have against changes in patient sizesurface and shape and require alignment, whichbeen may used become obstructed the linear accelerator Radiographic systems that overcome of are successfully to monitorbyintrafraction motion gantry. in several disease sites. However, these many systems these challenges exist [8],inbut they issue further unnecessary radiation dose when used, especially not robust against changes patient size and shape and require line-of-sight alignment, which may if used in real-time. Medical Technologies (now owned systems by Varian Medical Systems) become obstructed by theCalypso linear accelerator gantry. Radiographic that overcome many of developed a radiofrequency (RF) tracking system that utilizes transponders implanted in tumors to these challenges exist [8], but they issue further unnecessary radiation dose when used, especially if track the interior disease in real-time [8,9]. Although this system successfully meets this real-rime used in real-time. Calypso Medical Technologies (now owned by Varian Medical Systems) developed tracking goal and overcomes many of the disadvantages inherent to optical systems, the bulky RF a radiofrequency (RF) tracking system that utilizes transponders implanted in tumors to track the array is often cumbersome to use in the clinic and prevents the use of radiographic imaging while in interior disease in real-timegives [8,9].the Although systemanatomy successfully this real-rime tracking use, which definitively position this of interior rather meets than Calypso’s surrogate goal positions. and overcomes many of the disadvantages inherent to optical systems, the bulky RF array is Further, Calypso is constrained to extracranial sites, limiting its full clinical utility. Lastly, oftenwhile cumbersome to use inhave the clinic andinvolving preventsthe thesurgical use of implant radiographic imaging while of in use, few complications occurred of seeds, the necessity surgical procedures undesirable. which definitively givesis the position of interior anatomy rather than Calypso’s surrogate positions. In this paper, we introduceto a novel RF tracking system capable monitoring patient motionwhile Further, Calypso is constrained extracranial sites, limiting itsoffull clinical the utility. Lastly, in near real-time, which can overcome all of the aforementioned disadvantages. Such a system few complications have occurred involving the surgical implant of seeds, the necessity would of surgical consist of series of skin-wearable transmitters [10–12] gently affixed to a patient and an external procedures is undesirable. sensor network that tracks the patient position and attitude in real-time via estimate of the In this paper, we introduce a novel RF tracking system capable of monitoring the patient motion transmitters’ positions. RF waves have intrinsic advantages over other photonic means because radio in near real-time, which can overcome all of the aforementioned disadvantages. Such a system would waves readily propagate through many materials and do not deliver any radiation dose. In addition, consist of series of skin-wearable transmitters [10–12] to a patient an be external sensor such transmitters placed at strategic anatomical sites gently outsideaffixed of the radiation fieldand would resilient network thatthe tracks patient position and attitude via estimate of the transmitters’ against issuethe of skin deformation, normally seeninbyreal-time optical systems; identification of each positions. RF waves havefacilitates intrinsictracking advantages over other photonic means because radio waves transmitter on a patient multiple rigid bodies.
readily propagate through many materials and do not deliver any radiation dose. In addition, such transmitters placed at strategic anatomical sites outside of the radiation field would be resilient against the issue of skin deformation, normally seen by optical systems; identification of each transmitter on a patient facilitates tracking multiple rigid bodies.
Sensors 2016, 16, 534
3 of 11
2. Materials and Methods Sensors 2016, 16, 534
2.1. Localization System
3 of 11
2. Materials and Methods
We designed a localization system that uses the direction of arrival measurements in an RF sensor network to angulate 2.1. Localization System skin-wearable transmitters on a patient. This technique allows a precise localization We of transmitters, mounted on a that patient, without demanding strict timinginsuch as global designed a localization system uses the direction of arrival measurements an RF positioning system [13]. Many current approaches [14–16] measure the direction of arrival sensor network to angulate skin-wearable transmitters on a patient. This technique allows a preciseof an RF of transmitters, mounted onof a patient, withoutbetween demanding strict timing such as global arrays. signal bylocalization comparing the phase difference an RF wave elements in static antenna positioning system [13]. Many current approaches [14–16] measure the direction of arrival of RF We propose a similar system, but with two major variations: a rotating array platform andanoperating at signal by comparing the phase difference of an RF wave between elements in static antenna arrays. two significantly different frequencies. This sensor system can find the direction of patient-mounted We propose a similar system, but with two major variations: a rotating array platform and operating at transmitters in a 2D plane with high accuracy (~0.1˝ ). A generic prototype of this sensor design was two significantly different frequencies. This sensor system can find the direction of patient-mounted simulated by a programming language (MATLAB, Natick, MA, USA). A network of transmitters in a 2D plane with high accuracy (~0.1°).MathWorks, A generic prototype of this sensor design was sensors then usedby thea combined direction to find the location the A transmitters simulated programming languagemeasurements (MATLAB, MathWorks, Natick, MA, of USA). network of in a 2D sensors2a). thenAused the form combined direction measurements to find the location of the transmitters plane (Figure closed solution based on real measurements is extremely unlikelyintoa exist for 2D plane (Figure 2a). A closed form solution based on real measurements is extremely unlikely to any positioning system, so least squares estimation of the position is required. In order to estimate the exist for any positioning system, so least squares estimation of the position is required. In order to accuracy of the least squares solution, we used a Monte Carlo simulation. The simulation estimates estimate the accuracy of the least squares solution, we used a Monte Carlo simulation. The simulation the magnitude ofthe themagnitude positioning error based on the number sensors in the network and the estimates of the positioning error based on theof number of sensors in the network and angular resolution the sensors. theof angular resolution of the sensors.
Figure 2. (a) A network of sensors with antennas used in parallel to find the location of the transmitter
Figure 2.in(a) A network sensors withsends antennas used in parallel to find theantennas locationasofthey theturn transmitter a patient’s head.ofThe transmitter a radiofrequency (RF) signal to the in a patient’s head. transmitter sends a radiofrequency (RF) in signal to the The antennas as they turn through angleThe θ, which is measured individually by each antenna each sensor. gray arrows estimated direction individually of arrival by each projected in intoeach theirsensor. planes of rotation; throughrepresent angle θ,the which is measured by sensor each antenna The gray arrows (b)the Geometric abstract of a single having two antennas to find into the direction vector V represent estimated direction ofsensor arrival by each sensor used projected their planes ofofrotation; the transmitter. Ci, di, and αi refer to the distance from the center of the sensor to the i-th antenna, the (b) Geometric abstract of a single sensor having two antennas used to find the direction vector V of distance from the transmitter to the i-th antenna, and the angular position of i-th antenna, the transmitter. Ci , di , and αi refer to the distance from the center of the sensor to the i-th antenna, the respectively. Location t refers to the geometric location of the transmitter and location s refers to the distancelocation from the to the i-th The antenna, and position antenna,ofrespectively. of transmitter the center of the sensor. diameter of the the angular entire sensor is 2R. of Thei-th intersection the Locationdirection t refersvector to theVgeometric location the transmitter and location s refers to the location of the from each sensor findsofthe location of the transmitter. center of the sensor. The diameter of the entire sensor is 2R. The intersection of the direction vector V 2.2. Direction Arrival Measurements from each sensoroffinds the location of the transmitter. Figure 2b illustrates the geometry of the external sensor system. The system consists of two antennas placed atMeasurements opposite sides of a circle (diameter: 2R) which rotates around its central axis. The 2.2. Direction of Arrival relation between the signals received by these antennas determines the direction vector toward the
Figure 2b illustrates the geometry of the external The system consists of patient-mounted transmitter projected onto the 2D plane ofsensor rotation.system. Each transmitter on a patient emits a sine wave, for a given duration, which (diameter: consists of two2R) frequencies (1.5 and 48 GHz) asits a central two antennas placed atx(t), opposite sides of a circle which rotates around compromise between antenna spatial constraints and available spectra. As the sensor system rotates, axis. The relation between the signals received by these antennas determines the direction vector the signals from two antennas are multiplied together and the resultant amplitude is measured. In toward the patient-mounted transmitter projected onto the 2D plane of rotation. Each transmitter on the simulation, the transmitter was placed at origin and the center of the sensor was placed at two a patientmeters emits away a sineinwave, x(t), for a given duration, which consists of two frequencies (1.5 and 48 GHz) the horizontal plane and one meter above the plane of the transmitter. In a 2D plane, as a compromise between antenna spatial constraints and available spectra. As the sensor system rotates, the signals from two antennas are multiplied together and the resultant amplitude is measured. In the simulation, the transmitter was placed at origin and the center of the sensor was placed at two meters away in the horizontal plane and one meter above the plane of the transmitter. In a 2D
Sensors 2016, 16, 534
4 of 11
plane, this corresponds to the setup described in Figure 3. Because the lower frequency component has a wavelength equal to twice the length of the sensor’s diameter, the resultant interfered signal oscillates at the rate of the sensor rotation, and the angular position of the peak corresponds to the Sensors 2016, 16, 534 of 11 direction of arrival. The high frequency component creates a secondary oscillation with a4 predictable pattern that facilitates identification of the center of the peak (Figure 3). In a real setting in the treatment this corresponds to the setup described in Figure 3. Because the lower frequency component has room, one-half of a sensor rotation could be used as a coarse measurement to find the direction to a wavelength equal to twice the length of the sensor’s diameter, the resultant interfered signal ˝ , and then a high-resolution scan may be performed over a much smaller arc to find the nearest 5 oscillates at the rate of the sensor rotation, and the angular position of the peak corresponds to the ˝ ). This method can accurately determine the 2D the direction at of the limitations offrequency the method (~0.05creates direction arrival. The high component a secondary oscillation with a predictable pattern that facilitates center of the peak (Figure 3). angle In a real setting (greater in the projected direction of arrivalidentification vector evenofinthe cases where the out-of-plane is severe than treatment one-halfof ofthe a sensor rotation could be used as ashort coarse(6.6 measurement to find the in path 80˝ ). Because theroom, wavelength high frequency signal is very mm) the differences direction to the nearest 5°, and then a high-resolution scan may be performed over a much smaller length between the two antennas is still distinguishable. In our simulation, the following equation arc to find the direction at the limitations of the method (~0.05°). This method can accurately creates adetermine time-dynamic transmitted wave: the 2D projected direction of arrival vector even in cases where the out-of-plane angle is severe (greater than 80°). Because the wavelength of the high frequency signal is very short (6.6 mm) ptq “ between A1 sin p2π f 1 t `antennas ϕ1 q ` isAstill p2π f 2 t ` ϕ2 qIn our simulation, the 2 sin the differences in pathxlength the two distinguishable. following equation creates a time-dynamic transmitted wave:
(1)
where A is the amplitude of each of the two waves, f is the frequency of each wave, t is the sampled (1) = sin 2π + + sin 2π + point in time, and ϕ is the initial phase of each wave. The sine wave is sampled at 150 THz over where A is the amplitude of each of the two waves, f is the frequency of each wave, t is the sampled a 33 ns pulse. This corresponds to 50 wavelengths of the lower frequency and approximately point in time, and ϕ is the initial phase of each wave. 5The sine wave is sampled at 150 THz over 1500 wavelengths of the higher frequency over 2.5 ˆ 10 points, or 5000 points per wavelength of the a 33 ns pulse. This corresponds to 50 wavelengths of the lower frequency and approximately low frequency and approximately pointsover per 2.5 wavelength high frequency. This sampling rate 1500 wavelengths of the higher170 frequency × 105 points,oforthe 5000 points per wavelength of the was chosen as compromise between fully modeling the complete sine wave of theThis highsampling frequency and low frequency and approximately 170 points per wavelength of the high frequency. rate was chosen as compromise betweenphases fully modeling the complete sine wave of the high frequency conserving system memory. The starting of the wave components were chosen from a uniform and conserving system memory. The starting phases of the wave components were chosen from random distribution between 0 and 2π. The amplitudes of both waves are assumed equal in astrength. uniform random distribution between 0 and 2π. The amplitudes of both waves are assumed equal in The wavelength of the lower frequency component is calculated according to the speed of light in air, strength. The wavelength of the lower frequency component is calculated according to the speed of and is termed as the wavelength. light in air, and carrier is termed as the carrier wavelength.
Figure 3. Spatial geometry of a single sensor with two antennas at the selected locations and the
Figure 3. Spatial geometry of a single sensor with two antennas at the selected locations and the sensor’s signal response for one-half revolution (not to scale). The central peak of the signal shape sensor’srepresents signal response for one-half revolution (not to scale). The central peak of the signal shape the direction used for the narrow search. The three selected transmitter positions shown represents the direction used the narrow search. Thewith three selected positions are: (a) 90° with respect to for the coordinate system; (b) 135° respect to thetransmitter coordinate system, and; shown ˝ with respect to the coordinate system; and are: (a) (c) 90˝0°/180° with respect to the coordinate 135 with respect to the coordinatesystem; system. (b) In all cases, the distance between the center of the ˝ with sensor and respect the transmitter 2 meters in the horizontal plane and meter in the vertical the plane. (c) 0˝ /180 to thewas coordinate system. In all cases, the1distance between center of the sensor and the transmitter was 2 m in the horizontal plane and 1 meter in the vertical plane.
Sensors 2016, 16, 534
5 of 11
Vector analysis defines the location of the transmitter as point t in 3D space. The center of a given sensor is defined as point s, and the angular position of the i-th antenna in the plane of the sensor’s rotation is defined as αi . The vector V between the transmitter’s location and the center of the sensor is defined as: Vˆ “ s ´ t (2) The vectors from the center of the sensor to the i-th antenna receiver was then calculated for angular positions j: “ ‰ ˆ i,j “ R ˆ cosαi,j , sinαi,j , 0 C (3) The distance between the transmitter and each i-th receiver at every j-th sampled angular position was then found as the magnitude of the vector connecting between the transmitter and each receiver: ˆ i,j k di,j “ kVˆ ` C
(4)
This distance is then converted to fractions of the carrier wavelength, mi,j . At each angular position j, each receiver reads the transmitted signal after the respective number of carrier wavelengths of the transmitted signal, mi,j + M, for n wavelengths, where M represents the minimum number of carrier wavelengths to wait before the signal is read. This “wait” parameter was included to ensure the antennas did not attempt to read the signal before the first index in the transmitted signal. We used M = 5 and n = 10 over 2000 uniformly spaced angular positions between 0˝ and 180˝ in the simulation. In reality, the device will very likely rotate slower than the 37.5 kHz that this math suggests (10 periods of a 1.5 GHz wave per angle for 2000 angles per half revolution). We have chosen n = 10 wavelengths interfered at each angle as a compromise between obtaining sufficient signal to read the amplitude and data storage. In a practical implementation, this will be achieved through analog means. This process simulates the phase difference ϕ, measured between the two receiving antennas at the same instant. Uniform Gaussian white noise is added at a given signal-to-noise ratio (SNR). Real clinical settings contain numerous potential RF reflectors, which could cause a very noisy RF environment. Therefore, we used an SNR value of 2 as a pessimistic assumption. The signals were then multiplied and the resultant amplitude was recorded against each sensor angle αj. A median filter was used to smooth the resulting data. The “findpeaks” algorithm of MATLAB’s Signal Processing Toolbox [17] was then used to identify the locations of the signal peaks by taking the location of the local maxima as the location of the peak. This process was repeated over 5000 iterations in a 4˝ search space of the simulated transmitter’s known position to judge the accuracy of the direction finding algorithm. 2.3. Angulation Uncertainty Estimation Multiple sensors are required to localize each transmitter’s signal in 3D space. Figure 4a displays the general layout of a practical scenario including transmitters on a patient and an array of sensors surrounded in a treatment room. In our simulation, the external sensor locations were randomly distributed in a room-sized hemispherical shell, centered at the simulated transmitter, to investigate the relationship between the number of direction measurements and localization estimate. The polar and azimuthal coordinates of each sensor were selected in a uniform 2π space. The radial distance from the transmitter to each receiver was taken from a uniform distribution between 3.5 and 4.5 m; the approximate size of a treatment room. The relationship between the angular resolution of the sensors and the accuracy of the position estimate was investigated by performing multiple iterations of estimation based on the same physical setup but varying the magnitude of the uncertainty in the angular measurement (Figure 4b).
Sensors 2016, 16, 534
6 of 11
Sensors 2016, 16, 534
6 of 11
Figure 4. (a) Three-dimension rendering of sensor grid in the clinical setting. Transmitters are Figure 4. (a) Three-dimension rendering of sensor grid in the clinical setting. Transmitters are attached to the patient; (b) Rationale for creating the Monte Carlo simulation: angular uncertainty attached to the patient; (b) Rationale for creating the Monte Carlo simulation: angular uncertainty exists in direction measurements, which can lead to errors in the localization process; (c) Process of exists in direction measurements, which can lead to errors in the localization process; (c) Process the Monte Carlo simulation: angular uncertainty θ is created by adding a vector ΔX to the true vector of the Monte Carlo simulation: angular uncertainty θ is created by adding a vector ∆X to the true between sensor and transmitter V, resulting in a simulated mis-measurement of direction U. The vector between sensor and transmitter V, resulting in a simulated mis-measurement of direction U. vectors ΔXi are randomly selected from a 3D Gaussian distribution; (d) Continued process of the The vectors ∆Xsimulation: a 3D Gaussian distribution; Continued i are randomly Monte Carlo a leastselected squares from calculation is used to find the best-fit(d) intersection of process the mis- of themeasured Monte Carlo simulation: a least squares calculation is used to find the best-fit intersection direction vectors, Ui, and the error is taken as the difference between the intersectionsofofthe mis-measured direction vectors, Ui ,the andintersection the error isoftaken as the difference between intersections the mis-measured vectors Ui and the true vectors Vi. The error is the compared to the of theaverage mis-measured vectors U and the intersection of the true vectors V . The error is compared to the i θi. i angular uncertainty average angular uncertainty θ i .
We also investigated the relationship between the number of sensors and the physical arrangement of them. The initial 3D direction between each sensor transmitter was We also investigated the relationship betweenvectors the number of sensors and theand physical arrangement calculated as: of them. The initial 3D direction vectors between each sensor and transmitter was calculated as:
− = s ´p (5) Vˆ i “ ‖ i − ‖ (5) k si ´ p k where the position si represents the position of the i-th sensor and p represents the position of the where the position si torepresents the position of direction the i-th sensor and p represents the variation, position of transmitter. In order simulate uncertainty in the of arrival measurement spatial the∆X transmitter. to simulate uncertainty in theofdirection of arrival measurement spatial i,j was addedIn to order the transmitter’s position for direction arrival measurement where ∆Xi,j is taken variation, ∆X was added to the transmitter’s position for direction of arrival measurement σj from a 3D i,j Gaussian distribution of standard deviation σj (Figure 4c). Values ofwhere exponentially betweendistribution 1.5−28 and 1.5 m (0.012–440 mm) toσjobserve wideValues range of of σj ∆Xwere taken from a 3D Gaussian of−2 standard deviation (Figurea4c). i,j is varied angular resolutions. were varied exponentially between 1.5´28 and 1.5´2 m (0.012–440 mm) to observe a wide range of angular resolutions. −` + ∆ , `σ ˘˘ ˆ i,j σ j s ´ p ` ∆X (6) , = i ˆ ` `σ ˘˘ Ui,j “ (6) − + ∆ ˆ , k s ´ p ` ∆X σ k i
i,j
j
vectors least squaresestimate estimateofofthe theposition, position, ttjj, was calculated AA least squares calculatedbased basedon onthese thesenew newdirection direction vectors for each magnitude of angular resolution σ j . for each magnitude of angular resolution σj . ¸´1 ˜
˜
´ = ÿ −ˆ
tj “
I ´ Ui,j
i
,ˆ U
i,j
,T
¯
¯ ÿ´ − ˆ i,j,U ˆ i,j,T si I´U
¸
(7)
(7)
i
where I representsa a3 3ˆ×33identity identity matrix. matrix. The position was where I represents The magnitude magnitudeofofthe theerror errorininthe theestimated estimated position was j . then found for each level of σ then found for each level of σj . Error j “k tj ´ p k (8)
Sensors 2016, 2016, 16, 16, 534 Sensors 534
of 11 11 77 of
= − (8) For each level of σj , the average angular miss was calculated by taking the average of the dot For each level of σj, the average angular miss was calculated by taking the average of the dot product between the true direction vectors from the transmitter and sensors and the simulated miss. product between the true direction vectors from the transmitter and sensors and the simulated miss. ` ˘ ´1 U ˆ i,j ¨ Vˆ i θ j “= cos (9) (9) cos , ∙ forfor angular uncertainty andand waswas compared to the The mean angular angularmiss missθθserves servesasasa asurrogate surrogate angular uncertainty compared to 4d). This had 5000 for each j to obtain error in estimated position for each σj (Figure the error in estimated position for each σj (Figure 4d). process This process haditerations 5000 iterations forσeach σj to statistically acceptable rangesranges of error a given angular uncertainty. The number of sensors in total obtain statistically acceptable offor error for a given angular uncertainty. The number of sensors in varied by 5,by 50,5, and 500500 in the network. This calculation was total varied 50, and in the network. This calculation wasperformed performedtotoobserve observethe the effect effect of number of of vectors vectors available available for for angulation angulation analysis. analysis. increasing the number 3. Results 3. Results 3.1. Direction of 3.1. Direction of Arrival Arrival Measurements Measurements Figure Figure 5a 5a shows shows the the simulated simulated results results of of the the direction direction of of signal signal arrival. arrival. The The measured measured data data demonstrates that the product of signals from two rotating antennas in the external systemforms formsa demonstrates that the product of signals from two rotating antennas in the external system asignal signal that may easily identified signal a minimal 45˝ rotation that may be be easily identified [17].[17]. The The signal rises rises from from a minimal value value at 45° at rotation (when ˝ (when the antennas are in line with the signal path) to a maximum value at 135 rotation (when the the antennas are in line with the signal path) to a maximum value at 135° rotation (when the vector ˝ vector between the antennas is perpendicular to the signal direction). The pattern repeats every 180 between the antennas is perpendicular to the signal direction). The pattern repeats every 180° because because the sensor 2-fold rotational The interference between the mixed-frequency the sensor has 2-foldhas rotational symmetry.symmetry. The interference between the mixed-frequency signals (1.5 signals (1.5 + 48 GHz) creates a pattern as the antenna array platform rotates, the frequencies ratio of the + 48 GHz) creates a pattern as the antenna array platform rotates, and the ratio of and the two two frequencies determines the number signal peaks between 0˝ and 5a,b). 180˝ (Figure 5a,b). peak The central determines the number of signal peaksofbetween 0° and 180° (Figure The central of the peak of the mixed-frequency signal corresponds to the direction of signal arrival, which is located in mixed-frequency signal corresponds to the direction of signal arrival, which is located in angular angular space by the signal analysis. A peak-finding algorithm found the peak of the high-resolution space by the signal analysis. A peak-finding algorithm found the peak of the high-resolution signal; signal; based oniterations 5000 iterations this process, the program found the direction of the transmitter to based on 5000 of thisofprocess, the program found the direction of the transmitter to be ˝ ˝ ˝ be 134.99 ˘ 0.07 compared a ground-truth value of 135 (Figure 134.99° ± 0.07° compared to ato ground-truth value of 135° (Figure 5c). 5c).
Figure 5. (a) Sensor signal response for one-half rotation when the transmitter was located at 135° Figure 5. (a) Sensor signal response for one-half rotation when the transmitter was located at 135˝ with with respect to the coordinate system with signal-to-noise ratio (SNR) = 2; (b) Signal response for the respect to the coordinate system with signal-to-noise ratio (SNR) = 2; (b) Signal response for the 4˝ 4° high resolution scan area when the transmitter was at˝135° with respect to the coordinate system high resolution scan area when the transmitter was at 135 with respect to the coordinate system with with SNR = 2; (c) Histogram of the results of the direction-finding program used on the highSNR = 2; (c) Histogram of the results of the direction-finding program used on the high-resolution scan resolution (b). Overthe 5000 iterations, thethe program found direction to ofbe the134.99 transmitter ˝ ˘ 0.07to ˝ area in (b). scan Overarea 5000in iterations, program found direction of thethe transmitter be 134.99° ± 0.07° compared to a ground-truth value of 135°. ˝ compared to a ground-truth value of 135 .
Sensors 2016, 16, 534
8 of 11
3.2. Angulation Uncertainty Analysis Sensors 2016, 16, 534between the direction of signal arrival measurement angular uncertainty 8 of 11 The relationship and the mean 3.2. error of the position estimate presents the linear patterns (Figure 6a). The result shows Angulation Uncertainty Analysis that increased number of sensors (Figure 6b–d) improves the position estimation for a given angular The relationship between the direction of signal arrival measurement angular uncertainty and resolution,thebut follows a logarithmic rate of improvement. The logarithmic plot in Figure 6a shows mean error of the position estimate presents the linear patterns (Figure 6a). The result shows that that the slopes of areofparallel, which6b–d) means that the of estimation improvement with respect increasedlines number sensors (Figure improves therate position estimation for a given angular resolution, but follows a logarithmic rate of improvement. The logarithmic plot in Figure 6a shows to angular resolution is proportional to the number of direction estimates. Our system aims to achieve that the slopesless of lines are1parallel, that thethe ratesame of estimation withdose respectmargins in tracking sensitivity than mm, which whichmeans is about scale improvement as the typical to angular resolution is proportional to the number of direction estimates. Our system aims to achieve conformaltracking radiotherapy. Therefore, the direction of arrival sensors require an angular resolution sensitivity less than 1 mm, which is about the same scale as the typical dose margins in ´ 1.5 ˝ near 10 conformal degreesradiotherapy. (~0.03 ) toTherefore, achievethe thedirection ideal accuracy, which is based on the assumption of arrival sensors require an angular resolution near that the 10−1.5 degrees (~0.03°) achieve the ideal accuracy,of which is based onisthe assumption that the final the 1-mm final design will include 50tosensors. The criterion consistency based on maintaining include 50 criterion of consistency based on maintaining the 1-mm sensitivitydesign with will 50 sensors in sensors. 96% of The all estimates. Given thatisthis estimate is an order of magnitude sensitivity with 50 sensors in 96% of all estimates. Given that this estimate is an order of magnitude estimate, estimate, we conclude that our simulated sensor accuracy and precision is sufficient to track the we conclude that our simulated sensor accuracy and precision is sufficient to track the position ofposition a transmitter on a patient. of a transmitter on a patient.
6. (a) Relationship between angular precision and error in least squares estimation of the Figure 6. Figure (a) Relationship between angular precision and error in least squares estimation of the transmitter position. Filled area represents two standard deviations of Monte Carlo simulation results. transmitter position. Filled area represents two standard deviations of Monte Carlo simulation results. Better results are closer to the bottom of the graph, therefore worst-case scenarios for a given number Better results are closer to bound the bottom the area; graph, therefore worst-case scenarios for5-sensor a given number of sensors is upper for eachoffilled (b–d) Spatial distribution of sensors for the (b), 50-sensor andfilled 500-sensor (d), Spatial respectively. of sensors case is upper boundcase for(c), each area;case (b–d) distribution of sensors for the 5-sensor case (b), 50-sensor case (c), and 500-sensor case (d), respectively.
4. Discussion and Conlusions
In a clinical environment, RF-based tracking equipment is largely untested. Potential RF reflectors include radiotherapy linear accelerators and simulation computed tomography scanners. In this work, we have introduced a RFtracking localization system for is accurate tracking of patient motionRF in reflectors In a clinical environment, RF-based equipment largely untested. Potential radiotherapy, which would provide high accuracy and robustness even in situations where the true include radiotherapy linear accelerators and simulation computed tomography scanners. In this work, signal may be difficult to distinguish from the noise using RF waves. Our system also calls for the we have introduced a RF that localization system for accurate tracking of patient motion in radiotherapy, use of components operate in the K-band of the electromagnetic spectrum, which are not widely available in normal commercial channels and less investigated scientific andwhere engineering literature. which would provide high accuracy and robustness even ininsituations the true signal may be RF waves in this spectral range may have different propagation characteristics, which could difficult to distinguish from the noise using RF waves. Our system also calls for the use of components
4. Discussion and Conlusions
that operate in the K-band of the electromagnetic spectrum, which are not widely available in normal commercial channels and less investigated in scientific and engineering literature. RF waves in this spectral range may have different propagation characteristics, which could introduce multi-path noise. The use of these components theoretically provides a significant improvement to our measurements, which justifies their use in tracking patient motion.
Sensors 2016, 16, 534
9 of 11
We have used 2000 discrete angular points per half rotation for simulating the direction of arrival sensor. In a practical setting, we foresee a system where the sensor would continuously rotate at a constant speed (~10 Hz) while the signals from both antennas are interfered by analog means and the resulting signal is measured every 0.1˝ , for a total of 1800 data points per half rotation. This calls for a 36 kHz sampling rate, which we believe is feasible. Several transmitters could be used together by serial polling, though maintaining 10 Hz resolution necessary for measuring motion from breathing would require faster sampling rates. We observed that two parameters can reduce the error in the positioning estimation: improving the angular resolution and increasing the number of sensors. In our simulation of the angulation process, we chose to model the sensors in a uniformly distributed random pattern. This was done to solve for the generic case, because the physical arrangement of sensors was found to have very little impact on the result of the angulation, as long as the transmitter was not in a position past 85˝ above or below the plane of rotation. In a real setting, the sensors may be positioned in whatever manner is convenient for each individual clinic. Due to practicality reasons, the total number of sensors is constrained to be less than 100, and the receiver-transmitter distance is constrained by the treatment room geometry. Therefore, we have focused a great amount of effort into methods that can improve the angular resolution of our direction of arrival analysis software. Based on standard room sizes and assumption that about 50 sensors will be used, we estimate that an angular resolution near 0.03˝ is necessary to achieve position estimate errors less than 1 mm. We are optimistic that achieving the resolution of 0.01˝ is possible with better peak detection algorithms, even in poor SNR environments, which could lead to 1-mm accuracy while using fewer sensors. In a clinic, the metal gantry of a linear accelerator may move between some of the sensors and the transmitters, which can cause reflections of the RF signal and cause a misreport of the direction of arrival at those obstructed sensors. Since the position of the gantry is well-known at all times, the direction estimate from potentially obstructed sensors could be ignored for localization purposes. This is a potential strength over optical systems, which cannot ignore the input of a single camera if obstructed by the gantry and still provide useful localization information. Our proposed system has some limitations. Unlike radiographic techniques and the Calypso system, our technique only provides localization information about discrete points on the patient’s surface as opposed to information about the interior anatomy. Therefore, we suggest that our technique be used in conjunction with radiographic techniques for fraction-to-fraction setup to ensure that interior anatomy is well-aligned. Our system is designed to provide reliable intrafraction motion tracking as conveniently and comfortably as possible. We believe that the combination of the ability to freely choose localization points and the ability to track multiple rigid bodies provides a significant advantage over competing optical methods. The skin wearable transmitters also require further investigation. Patients will need to wear the transmitters over the course of the treatment, which may take several weeks. A few skin-wearable devices [12,18] have been demonstrated to maintain functionality while worn for up to two weeks, even with exercising, showering, and normal living conditions. Therefore, longer periods of wear may be feasible. Overall, we have introduced a new RF localization system that overcomes the main weaknesses of existing intrafraction motion tracking systems [5,19,20]. This system is robust against changes in patient anatomy and provides real-time tracking of changes in complex patient positioning, without requiring line-of-sight detection and avoiding extra dose to a patient. The practical implementation requires further investigation; the involvement of many mechanical components in sensors may require frequent maintenance. However, the analog nature of the system grants increased precision in measurement, which justifies the risk of maintenance. Future work will include the design of external sensors to implement this analytical and simulation study and skin-wearable electronics [12,18] mounted on a patient for signal transmission. Additionally, the system will include tracking the transmitter in 3D, likely by combining the measurements from two orthogonal 2D localization systems.
Sensors 2016, 16, 534
10 of 11
Acknowledgments: W.-H.Y. acknowledges startup funding from the School of Engineering, Virginia Commonwealth University. We thank the research development support from the Center for Rehabilitation Science and Engineering at Virginia Commonwealth University. Author Contributions: M.O., S.K., and W.-H.Y. conceived and designed the research; M.O. performed the analytical modeling and Monte Carlo simulation; M.O., S.K., and W.-H.Y. analyzed the data; M.O., S.K., and W.-H.Y. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
References 1.
2. 3.
4.
5. 6.
7. 8.
9.
10. 11.
12.
13. 14. 15. 16. 17.
Van Herk, M.; Remeijer, P.; Rasch, C.; Lebesque, J.V. The probability of correct target dosage: Dose-population histograms for deriving treatment margins in radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 2000, 47, 1121–1135. [CrossRef] Bert, C.; Metheany, K.G.; Doppke, K.; Chen, G.T. A phantom evaluation of a stereo-vision surface imaging system for radiotherapy patient setup. Med. Phys. 2005, 32, 2753–2762. [CrossRef] [PubMed] Bert, C.; Metheany, K.G.; Doppke, K.P.; Taghian, A.G.; Powell, S.N.; Chen, G.T. Clinical experience with a 3D surface patient setup system for alignment of partial-breast irradiation patients. Int. J. Radiat. Oncol. Biol. Phys. 2006, 64, 1265–1274. [CrossRef] [PubMed] Cho, H.L.; Park, E.T.; Kim, J.Y.; Kwak, K.S.; Kim, C.J.; Ahn, K.J.; Suh, T.S.; Lee, Y.K.; Kim, S.W.; Kim, J.K.; et al. Evaluation of radiotherapy setup accuracy for head and neck cancer using a 3-D surface imaging system. J. Instrum. 2013, 8, 1–11. [CrossRef] Gopan, O.; Wu, Q. Evaluation of the accuracy of a 3D surface imaging system for patient setup in head and neck cancer radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 2012, 84, 547–552. [CrossRef] [PubMed] Krengli, M.; Gaiano, S.; Mones, E.; Ballare, A.; Beldi, D.; Bolchini, C.; Loi, G. Reproducibility of patient setup by surface image registration system in conformal radiotherapy of prostate cancer. Radiat. Oncol. 2009, 4, 10. [CrossRef] [PubMed] Kim, S.; Akpati, H.C.; Kielbasa, J.E.; Li, J.G.; Liu, C.; Amdur, R.J.; Palta, J.R. Evaluation of intrafraction patient movement for CNS and head & neck IMRT. Med. Phys. 2004, 31, 500–506. [PubMed] Willoughby, T.R.; Kupelian, P.A.; Pouliot, J.; Shinohara, K.; Aubin, M.; Roach, M.; Skrumeda, L.L.; Balter, J.M.; Litzenberg, D.W.; Hadley, S.W.; et al. Target localization and real-time tracking using the calypso 4D localization system in patients with localized prostate cancer. Int. J. Radiat. Oncol. Biol. Phys. 2006, 65, 528–534. [CrossRef] [PubMed] Kupelian, P.; Willoughby, T.; Mahadevan, A.; Djemil, T.; Weinstein, G.; Jani, S.; Enke, C.; Solberg, T.; Flores, N.; Liu, D.; et al. Multi-institutional clinical experience with the calypso system in localization and continuous, real-time monitoring of the prostate gland during external radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 2007, 67, 1088–1098. [CrossRef] [PubMed] Fan, J.A.; Yeo, W.H.; Su, Y.W.; Hattori, Y.; Lee, W.; Jung, S.Y.; Zhang, Y.H.; Liu, Z.J.; Cheng, H.Y.; Falgout, L.; et al. Fractal design concepts for stretchable electronics. Nat. Commun. 2014, 5, 3266. [CrossRef] [PubMed] Jang, K.I.; Han, S.Y.; Xu, S.; Mathewson, K.E.; Zhang, Y.H.; Jeong, J.W.; Kim, G.T.; Webb, C.; Lee, J.W.; Dawidczyk, T.J.; et al. Rugged and breathable forms of stretchable electronics with adherent composite substrates for transcutaneous monitoring. Nat. Commun. 2014, 5, 4779. [CrossRef] [PubMed] Norton, J.J.S.; Lee, D.S.; Lee, J.W.; Lee, W.; Kwon, O.; Won, P.; Jung, S.Y.; Cheng, H.Y.; Jeong, J.W.; Akce, A.; et al. Soft, curved electrode systems capable of integration on the auricle as a persistent brain-computer interface. Proc. Natl. Acad. Sci. USA 2015, 112, 3920–3925. [CrossRef] [PubMed] Dardari, D.; Falletti, E.; Luise, M. Satellite and Terrestrial Radio Positioning Techniques: A Signal Processing Perspective; Elsevier Ltd.: Oxford, UK, 2012. Amundson, I.; Sallai, J.; Koutsoukos, X.; Ledeczi, A. Mobile sensor waypoint navigation via rf-based angle of arrival localization. Int. J. Distrib. Sens. Netw. 2012, 1–15. [CrossRef] Dagefu, F.T.; Oh, J.; Sarabandi, K. A sub-wavelength rf source tracking system for GPS-denied environments. IEEE Trans. Antennas Propag. 2013, 61, 2252–2262. [CrossRef] Gorcin, A.; Arslan, H. A two-antenna single RF front-end doa estimation system for wireless communications signals. IEEE Trans. Antennas Propag. 2014, 62, 5321–5333. [CrossRef] Findpeaks. Available online: http://www.webcitation.org/6frMf9wsA (accessed on 8 March 2016).
Sensors 2016, 16, 534
18.
19.
20.
11 of 11
Yeo, W.H.; Kim, Y.S.; Lee, J.; Ameen, A.; Shi, L.K.; Li, M.; Wang, S.D.; Ma, R.; Jin, S.H.; Kang, Z.; et al. Multifunctional epidermal electronics printed directly onto the skin. Adv. Mater. 2013, 25, 2773–2778. [CrossRef] [PubMed] Linthout, N.; Verellen, D.; Tournel, K.; Storme, G. Six dimensional analysis with daily stereoscopic X-ray imaging of intrafraction patient motion in head and neck treatments using five points fixation masks. Med. Phys. 2006, 33, 504–513. [CrossRef] [PubMed] Chen, A.M.; Cheng, S.; Farwell, D.G.; Luu, Q.; Donald, P.J.; Boggan, J.; Franklin, S.; Purdy, J.A. Utility of daily image guidance with intensity-modulated radiotherapy for tumors of the base of skull. Head Neck Oncol. 2012, 34, 763–770. [CrossRef] [PubMed] © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
